Better Hotels
The hourly hotels are too disgusting to consider, plus if you're trying to be at all discreet, you've already given up the game by being seen going into one.
I've found that, with the economy as bad as it is, you can find pretty good rates at better hotels, maybe a three-star on the Orbitz scale. The tourist and business cycles are not usually in sync, so either the hotels in east midtown, which cater to business travelers, or the hotels on the west side, who usually cater to tourists, are available and cheap.
If occupancy rates are low, hotels usually get cheaper the longer you wait, with the best rates being posted the day before or the day of your stay. If they're high, then you've got to book early, but then they may be too expensive for this purpose.
Good luck with Jesse!!! He's such a favorite on this board, I'm sure it's worth the extra to meet in a nicer place.